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Advances in Mathematical Physics
Volume 2017, Article ID 7042686, 9 pages
https://doi.org/10.1155/2017/7042686
Research Article

Solutions of Navier-Stokes Equation with Coriolis Force

1Department of Advanced Materials and Chemical Engineering, Catholic University of Daegu, Gyeongsan, Gyeongbuk 38430, Republic of Korea
2Korea Institute of Energy Research, Daejeon 305-343, Republic of Korea

Correspondence should be addressed to Shin-Kun Ryi; rk.er.reik@enarbmem2h and Hankwon Lim; rk.ca.uc@milkh

Received 15 April 2017; Accepted 3 July 2017; Published 14 August 2017

Academic Editor: Eugen Radu

Copyright © 2017 Sunggeun Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, . In both steady state and two-dimensional flow, the vorticity vector gets shifted by the amount of . Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow , the equation satisfied by is independent of . The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of .